An integrator is a component whose output signal is the time integral of its input signal. An integrator is a version of a counter, cumulating the input into an output. An integrator is a basic building block of a sigma-delta modulator based analog-to-digital converters (ADC). A Sigma-delta modulator based ADC oversamples a desired signal by a factor and filters the desired signal band. A higher order (e.g., a second or higher order) sigma-delta modulator based ADC has at least two integrators. The integrators in the sigma-delta modulator based ADC behave as low-pass filters.
An ADC (e.g., a flash ADC) in the sigma-delta modulator based ADC is used to convert the output of a chain of integrators to a digital code. The resulting digital code, along with the error generated by the discrete levels of the ADC, is fed back and subtracted from the input of the integrators. This negative feedback has the effect of noise shaping the error due to the ADC so that it does not appear in the desired signal frequencies. Because the quantization noise is introduced at the ADC, which is within the feedback loop of the sigma-delta modulator based ADC, the transfer function from the input of the ADC to its output is a high pass filter, which creates the high pass noise shaping.
Sigma-delta modulator based ADC with orders of two or higher suffer from overload instability. Here, overload instability or overload condition is a condition where an input signal saturates the ADC, and so the output of the sigma-delta modulator based ADC begins to oscillate forever. For example, the input current into each integrator of the sigma-delta modulator based ADC becomes larger than the feedback current subtracted off from the input current. As a result, the outputs of the integrators drive to power supply and ground rails. As such, the ADC within the sigma-delta modulator based ADC tries to “race to catchup” to remove the extra charge on the capacitors of the integrators, but fails. The failure of the feedback loop to remove the extra charge causes the sigma-delta modulator based ADC to become unstable (i.e., output of Sigma-delta modulator based ADC oscillates forever).